Direct linear transformation: Difference between revisions

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where <math> \mathbf{x}_{k} </math> and <math> \mathbf{y}_{k} </math> are known vectors, <math> \, \propto </math> denotes equality up to an unknown scalar multiplication, and <math> \mathbf{A} </math> is a matrix (or linear transformation) which contains the unknowns to be solved.

This type of relation appears frequently in [[projective geometry]]. Practical examples include the relation between 3D points in a scene and their projection onto the image plane of a [[Pinhole camera model|pinhole camera]],<ref>{{cite journal | last=Abdel-Aziz | first=Y.I. | last2=Karara | first2=H.M. | title=Direct Linear Transformation from Comparator Coordinates into Object Space Coordinates in Close-Range Photogrammetry | journal=Photogrammetric Engineering & Remote Sensing | publisher=American Society for Photogrammetry and Remote Sensing | volume=81 | issue=2 | date=2015-02-01 | issn=0099-1112 | doi=10.14358/pers.81.2.103 | pages=103–107| doi-access=free }}</ref> and [[Homography (computer vision)|homographies]].

== Introduction ==

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== External links ==

* [httpshttp://wwwciteseerx.csist.ubcpsu.caedu/gradsviewdoc/resources/thesis/May09/Dubrofsky_Elansummary?doi=10.1.1.186.pdf4411 Homography Estimation] by Elan Dubrofsky (§2.1 sketches the "Basic DLT Algorithm")

* [http://www.mathworks.com/matlabcentral/fileexchange/65030-direct-linear-transformation--dlt--solver A DLT Solver based on MATLAB] by Hsiang-Jen (Johnny) Chien